Lindel\"of's hypothesis is true and Riemann's one is not

TL;DR

This paper provides a straightforward proof confirming Lindelöf's hypothesis for the Riemann zeta-function, and uses this to disprove Riemann's hypothesis through classical results.

Contribution

It offers an elementary proof of Lindelöf's hypothesis and demonstrates that Riemann's hypothesis does not hold based on established classical results.

Findings

Lindelöf's hypothesis is proven true.

Riemann's hypothesis is disproved.

Classical results support the conclusions.

Abstract

We present an elementary, short and simple proof of the validity of the Lindel\"of hypothesis about the Riemann zeta-function. The obtained estimate and classical results by Bohr-Landau and Littlewood disprove Riemann's hypothesis.